A General Expression for Predicting Conduction Shape Factors

1990 ◽  
Vol 55 (7) ◽  
pp. 1691-1707 ◽  
Author(s):  
Miloslav Karel ◽  
Jiří Hostomský ◽  
Jaroslav Nývlt ◽  
Axel König

Crystal growth rates of copper sulphate pentahydrate (CuSO4.5 H2O) determined by different authors and methods are compared. The methods included in this comparison are: (i) Measurement on a fixed crystal suspended in a streaming solution, (ii) measurement on a rotating disc, (iii) measurement in a fluidized bed, (iv) measurement in an agitated suspension. The comparison involves critical estimation of the supersaturation used in measurements, of shape factors used for data treatment and a correction for the effect of temperature. Conclusions are drawn for the choice of values to be specified when data of crystal growth rate measurements are published.


Molecules ◽  
2020 ◽  
Vol 26 (1) ◽  
pp. 149
Author(s):  
Karol Leluk ◽  
Stanisław Frąckowiak ◽  
Joanna Ludwiczak ◽  
Tomasz Rydzkowski ◽  
Vijay Kumar Thakur

Recently, biocomposites have emerged as materials of great interest to the scientists and industry around the globe. Among various polymers, polylactic acid (PLA) is a popular matrix material with high potential for advanced applications. Various particulate materials and nanoparticles have been used as the filler in PLA based matrix. One of the extensively studied filler is cellulose. However, cellulose fibres, due to their hydrophilic nature, are difficult to blend with a hydrophobic polymer matrix. This leads to agglomeration and creates voids, reducing the mechanical strength of the resulting composite. Moreover, the role of the various forms of pure cellulose and its particle shape factors has not been analyzed in most of the current literature. Therefore, in this work, materials of various shapes and shape factors were selected as fillers for the production of polymer composites using Polylactic acid as a matrix to fill this knowledge gap. In particular, pure cellulose fibres (three types with different elongation coefficient) and two mineral nanocomponents: precipitated calcium carbonate and montmorillonite were used. The composites were prepared by a melt blending process using two different levels of fillers: 5% and 30%. Then, the analysis of their thermomechanical and physico-chemical properties was carried out. The obtained results were presented graphically and discussed in terms of their shape and degree of filling.


2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Martin Fluder ◽  
Christoph F. Uhlemann

Abstract Renormalization group flows are studied between 5d SCFTs engineered by (p, q) 5-brane webs with large numbers of external 5-branes. A general expression for the free energy on S5 in terms of single-valued trilogarithm functions is derived from their supergravity duals, which are characterized by the 5-brane charges and additional geometric parameters. The additional geometric parameters are fixed by regularity conditions, and we show that the solutions to the regularity conditions extremize a trial free energy. These results are used to survey a large sample of $$ \mathcal{O} $$ O (105) renormalization group flows between different 5d SCFTs, including Higgs branch flows and flows that preserve the SU(2) R- symmetry. In all cases the free energy changes monotonically towards the infrared, in line with a 5d F -theorem.


The paper is a continuation of the last paper communicated to these 'Proceedings.' In that paper, which we shall refer to as the first paper, a more general expression for space curvature was obtained than that which occurs in Riemannian geometry, by a modification of the Riemannian covariant derivative and by the use of a fifth co-ordinate. By means of a particular substitution (∆ μσ σ = 1/ψ ∂ψ/∂x μ ) it was shown that this curvature takes the form of the second order equation of quantum mechanics. It is not a matrix equation, however but one which has the character of the wave equation as it occurred in the earlier form of the quantum theory. But it contains additional terms, all of which can be readily accounted for in physics, expect on which suggested an identification with energy of the spin.


1988 ◽  
Vol 110 (1) ◽  
pp. 264-266 ◽  
Author(s):  
T. L. Eddy ◽  
G. E. Nielsson
Keyword(s):  

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